Efficient simulation of Brown‒Resnick processes based on variance reduction of Gaussian processes. (29th November 2018)

• Record Type: Journal Article
• Authors: Oesting, Marco; Strokorb, Kirstin
• Is Part Of: Advances in applied probability. Volume 50:Number 4(2018)
• Page Start: 1155
• Page End: 1175
• Publication Date: 2018-11-29
• Subjects: Brown‒Resnick process, -- Gaussian process, -- max-stable process, -- simulation, -- spatial extremes, -- variance reduction, -- variogram; Primary 60G70, -- 60G15, -- Secondary 60G60; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2018.54
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: Brown‒Resnick processes are max-stable processes that are associated to Gaussian processes. Their simulation is often based on the corresponding spectral representation which is not unique. We study to what extent simulation accuracy and efficiency can be improved by minimizing the maximal variance of the underlying Gaussian process. Such a minimization is a difficult mathematical problem that also depends on the geometry of the simulation domain. We extend Matheron's (1974) seminal contribution in two directions: (i) making his description of a minimal maximal variance explicit for convex variograms on symmetric domains, and (ii) proving that the same strategy also reduces the maximal variance for a huge class of nonconvex variograms representable through a Bernstein function. A simulation study confirms that our noncostly modification can lead to substantial improvements among Gaussian representations. We also compare it with three other established algorithms.